Consensus analysis of multi-agent systems with general linear dynamics and switching topologies by non-monotonically decreasing Lyapunov function

Abstract

This paper investigates consensus problems for multi-agent systems with general linear dynamics and switching topologies. In order to deal with the intricate interaction between dynamics of isolated agents and switching-disconnected topologies, the consensus analysis is performed by non-monotonically decreasing Lyapunov function. Particularly, the design of consensus laws is explored from the perspective of fast time-varying systems with two time scales. Sufficient conditions for achieving consensus are derived, which depend on not only feedback gains and connectivity of network topologies but also the speed of topology switching and the stability of individual agent. Therefore consensus laws are generalized in the sense that the dynamics of linear agents are allowed to be unstable and switching topologies are allowed to be jointly weakly connected and balanced. Finally, numerical simulations are provided to demonstrate the effectiveness of theoretical results.